Cos 1080 Degrees

The value of cos 1080 degrees is 1. Cos 1080 degrees in radians is written as cos (1080° × π/180°), i.e., cos (6π) or cos (18.849555. . .). In this article, we will discuss the methods to find the value of cos 1080 degrees with examples.

• Cos 1080°: 1
• Cos (-1080 degrees): 1
• Cos 1080° in radians: cos (6π) or cos (18.8495559 . . .)

What is the Value of Cos 1080 Degrees?

The value of cos 1080 degrees is 1. Cos 1080 degrees can also be expressed using the equivalent of the given angle (1080 degrees) in radians (18.84955 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1080 degrees = 1080° × (π/180°) rad = 6π or 18.8495 . . .
∴ cos 1080° = cos(18.8495) = 1

Explanation:

For cos 1080°, the angle 1080° > 360°. Given the periodic property of the cosine function, we can represent it as cos(1080° mod 360°) = cos(0°). The angle 1080°, coterminal to angle 0°, lies on the positive x-axis.
Thus, cos 1080 degrees value = 1
Similarly, cos 1080° can also be written as, cos 1080 degrees = (1080° + n × 360°), n ∈ Z.
⇒ cos 1080° = cos 1440° = cos 1800°, and so on.
Note: Since, cosine is an even function, the value of cos(-1080°) = cos(1080°).

Methods to Find Value of Cos 1080 Degrees

The value of cos 1080° is given as 1. We can find the value of cos 1080 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 1080 Degrees Using Unit Circle

To find the value of cos 1080 degrees using the unit circle, represent 1080° in the form (3 × 360°) + 0° [∵ 1080°>360°] ∵ cosine is a periodic function, cos 1080° = cos 0°.

• Rotate ‘r’ anticlockwise to form 1080° or 0° angle with the positive x-axis.
• The cos of 1080 degrees equals the x-coordinate(1) of the point of intersection (1, 0) of unit circle and r.

Hence the value of cos 1080° = x = 1

Cos 1080° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 1080 degrees as:

• ± √(1-sin²(1080°))
• ± 1/√(1 + tan²(1080°))
• ± cot 1080°/√(1 + cot²(1080°))
• ±√(cosec²(1080°) - 1)/cosec 1080°
• 1/sec 1080°

Note: Since 1080° lies on the positive x-axis, the final value of cos 1080° will be positive.

We can use trigonometric identities to represent cos 1080° as,

• -cos(180° - 1080°) = -cos(-900°)
• -cos(180° + 1080°) = -cos 1260°
• sin(90° + 1080°) = sin 1170°
• sin(90° - 1080°) = sin(-990°)

☛ Also Check:

• cos 30 degrees
• cos 2 degrees
• cos 45 degrees
• cos 14 degrees
• cos 230 degrees
• cos 390 degrees

FAQs on Cos 1080 Degrees

What is Cos 1080 Degrees?

Cos 1080 degrees is the value of cosine trigonometric function for an angle equal to 1080 degrees. The value of cos 1080° is 1.

How to Find the Value of Cos 1080 Degrees?

The value of cos 1080 degrees can be calculated by constructing an angle of 1080° with the x-axis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of cos 1080° is equal to the x-coordinate (1). ∴ cos 1080° = 1.

How to Find Cos 1080° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 1080° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(1080°))
• ± 1/√(1 + tan²(1080°))
• ± cot 1080°/√(1 + cot²(1080°))
• ± √(cosec²(1080°) - 1)/cosec 1080°
• 1/sec 1080°

☛ Also check: trigonometric table

What is the Value of Cos 1080 Degrees in Terms of Sin 1080°?

Using trigonometric identities, we can write cos 1080° in terms of sin 1080° as, cos(1080°) = √(1 - sin²(1080°)). Here, the value of sin 1080° is equal to 0.

What is the Exact Value of cos 1080 Degrees?

The exact value of cos 1080 degrees is 1.